# Solar mass

The solar mass , M ☉ for short , is an astronomical unit of measurement that is defined by the mass of the sun . It amounts to:

 ${\ displaystyle 1 \, \ mathrm {M _ {\ odot}} = (1 {,} 98892 \ \ pm \ 0 {,} 00025) \ \ cdot 10 ^ {30} \, \ mathrm {kg}}$

This corresponds to 1.99 quintillion kg or 332,946 earth masses .

The unit of solar mass is used to indicate the mass of astronomical objects that are more massive than planets . This includes, for example, stars and star clusters , massive gas nebulae and dark nebulae , galaxy nuclei, black holes or entire galaxies . The masses of galaxy clusters or the observable universe are given in terms of solar masses less often .

Most other stars have masses between 0.1 and 10 solar masses. The mass of the sun is therefore in the average of the masses of the main sequence stars . Occasionally there are also significantly more massive stars with up to 250 solar masses, e.g. B. R136a1 in the tarantula nebula .

## determination

With the help of Kepler's third law , the mass of the sun can be calculated from the major semiaxis of the earth's orbit and the period of the earth's orbit . The following applies: ${\ displaystyle a}$${\ displaystyle T}$${\ displaystyle M _ {\ odot}}$

 ${\ displaystyle \ mathrm {M _ {\ odot}} = {\ frac {4 \ pi ^ {2} \ cdot a ^ {3}} {G \ cdot T ^ {2}}}}$

Here is the gravitational constant . ${\ displaystyle G}$

The approximation is only valid if the mass of the rotating body is significantly smaller than the mass of the central body. This is the case with the earth and the sun. Inserted results in:

 ${\ displaystyle \ mathrm {M _ {\ odot}} = {\ frac {4 \ pi ^ {2} \ cdot (1 \, {\ text {AE}}) ^ {3}} {G \ cdot (1 \ , {\ text {yr}}) ^ {2}}}}$

The gravitational constant must be known for the calculation. It is one of the most difficult constants of nature to determine because the gravitational force is extremely weak compared to the other basic forces . Today the value is known to be 4 to 5 significant digits; this is very imprecise in comparison to other natural constants. The first measurement of the gravitational constant was made by Henry Cavendish in 1798 . Before that, only the product of the earth's mass and the gravitational constant was known. Therefore, the solar mass could only be given in multiples of the earth's mass or, conversely, the earth's mass in fractions of the solar mass.

Because of the historical fact that the solar mass was not known and therefore the masses of many objects (e.g. planets) had to be specified in solar masses, but also because of the more manageable numerical values ​​this unit is still in use today.

The solar mass gradually decreases through the nuclear fusion of hydrogen to helium nuclei. The mass difference during the fusion is about 4.3 million tons per second and is released as radiation. In addition, a quarter of this amount comes from the solar wind .

The secular increase in solar luminosity as a result of rising temperature is also of long-term importance . It is estimated to be a few percent in 500 million years.

## Related units

One solar mass corresponds to:

The Milky Way has about 180 billion solar masses, which corresponds to approx. 3.6 · 10 41  kg. For other galaxies , such information is still very uncertain and is currently only known for nearby, well-measured systems.

In the general theory of relativity , it is sometimes common to specify the mass in units of length. The following applies (with the gravitational constant G and the speed of light c ):

 ${\ displaystyle \ mathrm {M _ {\ odot}} {\ frac {G} {c ^ {2}}} \ approx 1 {,} 48 ~ \ mathrm {km}}$